Process for the noncoherent demodulation of a digital signal

ABSTRACT

The present invention relates to a process for the noncoherent demodulation of a linearly modulated digital signal with energy by constant symbol and a demodulator for performing this process. The process consists of demodulating a linearly modulated signal by a sequence of information symbols α 0 , . . . , α N-1  to which has been added a Gaussian white noise. The signal received is processed by the demodulator in order to obtain sequences of blocks of L data, containing all the information of the received signal. By means of a recursive algorithm, from said data is deduced a sequence of symbols α 0 , . . . , α N-1 , maximizing an approximate probability function. The invention more particularly applies to satellite links and to vehicle radio communications.

BACKGROUND OF THE INVENTION

The present invention relates to a process for the noncoherentdemodulation of a linearly modulated signal where each symbol α_(k) hasthe same energy and a demodulator for performing this process. It ismore particularly used in satellite links and in vehicle radiocommunications.

A digital signal x(t), in which t is a time variable, is generally anarrow band signal centered about a frequency f₀ called the carrierfrequency and of band width B. It is therefore a signal, whose spectraldensity is zero outside the frequency spacing, [f₀ -B/2, f₀ +B/2].

In signal theory, it is standard practice to represent this digitalsignal by its complex envelope α(t), the relation between x(t) and α(t)being given by the equation

    x(t)=Re(α(t).e.sup.jw.sbsp.0.sup.t)

in which Re signifies "real part of", e signifies exponential and j is acomplex number, such as j² =-1 and w₀ is the ripple corresponding to thefrequency f₀. As the complex representation permits a clearerdefinition, it will be used throughout the remainder of the text.

Consideration will be given to a sequence of N symbols a₀, . . . ,a_(k), . . . , a_(N-1) where k is an integer and where each a_(k)represents an information to be transmitted, where N equalsapproximately 64. These symbols are elements of an e.g. binary alphabetA. For minimizing the error rate in transmitting the sequence of symbolsa₀ . . . a_(N-1), it is standard practice to encode this sequence intoanother sequence of symbols α₀ . . . α_(N-1) in which each symbol ofsaid other sequence belongs to another alphabet α, which is e.g. of theM-type, in which M is an integer.

This sequence of symbols α₀ . . . α_(N-1) will effectively betransmitted by a modulated signal, the modulation being realized by thesaid signals. In the case of a linear modulation, the complex envelopeα(t) of the modulated signal x(t) containing the information to betransmitted is then represented by the expression ##EQU1## in which T isthe time interval between the transmission of two successive symbols andg(t) is a function, with real or complex values, describing the pulseresponse of all the emission filters so that |α_(k) |² =1 and ##EQU2##dt, equal to E_(b) is the energy per bit.

FIG. 1 is a diagrammatic representation illustrating the known chain ofmodulation, transmission and demodulation of symbols a₀ . . . a_(N-1),which are sequentially received in a modulator 2. They follow oneanother spaced by a time interval T. The modulator 2 comprises a codingmeans 4 supplying at the output the sequence of symbols α₀ . . .α_(N-1), which are spaced from one another by a time interval T. It alsocomprises a modulation means 6, which supplies the complex envelope α(t)in the form of its real part, Re(α(t)) and its imaginary part Im(α(t)).These two signals are frequency inverted by respectively modulating asignal cos (w₀ t) supplied by an oscillator 8 and a signal -sin (w₀ t)supplied by a phase shifter 10, which is connected by the input tooscillator 8. The two resulting modulated signals are summated and theirsum constitutes the emitted signal x(t).

This emitted signal x(t) during transmission, is subject todisturbances, represented by the addition of a Gaussian white noise b(t)of bilateral spectral density N₀ /2 in watt/hertz. Thus, demodulator 12receives a signal y(t) equal to x(t)+b(t), which is frequency reinvertedby modulating a first signal 2. cos (w₀.t+θ(t)) from an oscillator 14and a second signal -2. sin (w₀.t+θ(t)) supplied by a phase shifter 16,which is connected to the same oscillator 14. The phase θ(t) of thesignals is now known in the case of a non-coherent demodulation, but itsvariation is slow compared with the binary flow rate of transmission.The modulated signals are respectively designated Re(r(t)) and Im(r(t)).These are the real and imaginary components of the complex envelope r(t)of the signal y(t). These signals are filtered by a matched filteringmeans 18 of pulse response g(t₀ -t), in which t₀ is a quantitycharacterizing the transmission time of the signal all along the chain.A means 20 then samples these signals and supplies at the output thereal part Re(r_(k) ) and imaginary part Im(r_(k)) of the observationr_(k) in which 0≦k≦N-1. This means 20 performs a sampling at datesseparated by a time interval T.

The observations r₀ . . . r_(N-1) are sequentially applied to the inputof a calculating or computing means 22, which supplies at the output asequence of symbols α₀ . . . α_(N-1) which represent the most probableestimated values of the symbols α₀ . . . α_(N-1) emitted, bearing inmind the observations r₀ . . . r_(N-1). If the transmission of thesymbols α₀ . . . α_(N-1) is perfect, the symbols α₀ . . . α_(N-1) arerespectively identical to said symbols α₀ . . . α_(N-1). The sequence ofsymbols α₀ . . . α_(N-1) obtained is then decoded by a decoding means24, which supplies a sequence of symbols a₀ . . . a_(N-1). The latterare respectively identical to the symbols a₀ . . . a_(N-1), if thetransmission is perfect.

The demodulation performed is said to be noncoherent if the phase θ(t)of the signal emitted by oscillator 14 is not known. This isparticularly the case if this oscillator is free, i.e. if it is notdependent on the signal received y(t).

In general terms, the demodulation, i.e. the determination of the mostprobable sequence of symbols α₀ . . . α_(N-1) minimizes the error rateon reception, if the symbols emitted are equiprobable. It is known fromthe article "Optical Reception of Digital Data over the Gaussian Channelwith Unknown Delay and Phase Jitter" by David D. Falconer, whichappeared in IEEE Transactions on Information Theory, January 1977, pp.117-126, that the probability function in coherent reception maximizes:##EQU3## as a function of the symbols α₀ . . . α_(N-1), in which r*(t)is the conjugate complex of r(t) and in which θ(t) characterized thephase introduced by the transmission channel.

This maximization cannot be performed in the case of a coherentdemodulation in which θ(t) is a known function of the receiver, whichcan thus be assumed as zero. In the case of a noncoherent demodulation,it can be maximized if it assumed, and this is a reasonable hypothesis,that θ(t) is constant over the time interval [0,NT] and is considered bythe receiver as a random variable equally distributed on [0,2π] saidconstant being unknown to the receiver. It is known that the quantitymaximized is then ##EQU4##

By replacing α(t, α₀, . . . , α_(N-1)) by ##EQU5## and on noting thatthe square of the absolute value of a complex number is equal to theproduct of this complex number by its conjugate, it is possible toreplace the quantity to be maximized by the equivalent quantity ##EQU6##

The receiver or demodulator determining the sequence of symbols α₀ . . ., α_(N-1) maximizing this quantity is said to be optimum in the sense ofthe probability maximum. In practice, the maximization is of a risingcomplexity with N (the calculation number rises as 2^(N)) and for Nhigher than about 10, it is not known how this expression can be solvedin a simple manner.

Several methods are known which make it possible to obtain a suboptimumreceiver. It is possible to choose an observation window formed by asingle symbol (N=1). This leads to the conventional noncoherentreceiver, more particularly used in low speed modems, which observe thesignal symbol by symbol.

A noncoherent receiver using a two symbol observation window is alsoknown. in the case of phase shift keying (PSK), this receiver is theconventional differential receiver.

A noncoherent receiver using an observation window of two 2P+1 symbols,in which P is an integer, is known for determining the central symbol.This method described in the article "Coherent and noncoherent detectionof CPDSK" by W. P. Osborne and M. B. Luntz, which appeared in IEEETransactions on Communications, vol. COM-22, no. 8, August 1974, pp.1023-1036 leads to a receiver which cannot be produced, because theprobability function is not expressed in a simpler manner as a functionof the observation.

SUMMARY OF THE INVENTION

The present invention obviates the deficiencies of known receivers byusing a simpler approximate function of the probability function, whichcan be maximized in a recursive manner. This method is particularlysuitable for the transmission of blocks of symbols of considerablelength (N=64 for example). The receiver associated with this functionhas very good performance characteristics in the sense of the errorrate.

The invention more particularly consists of modifying the quantity to bemaximized referred to hereinbefore in such a way as to easily find asequence α₀, . . . , α_(N-1) maximizing the same. In particular, thequantity to be maximized is replaced by the quantity V(α₀, . . . ,α_(N-1)) equal to ##EQU7## which can also be written ##STR1## if thesymbols α_(o) . . . α_(N-1) are real numbers. In these two expressionsk-l remains between 0 and N-1. The value of L is predetermined, and ise.g. between 1 and 5.

It is obvious that as the quantity to be maximized has been truncated##EQU8## being replaced by ##EQU9## the sequence of symbols α₀, . . . ,α_(N-1) maximizing the simplified quantity V(α₀, . . . , α_(N-1)) is nolonger decided in an optimum manner and is instead decided in asuboptimum manner. This in particular means that the error rate of theassociated receiver is higher than that of the theoretical receiverassociated with the non-truncated expression. This error rate varieswith L, but has an asymptotic tendency towards the rate of the optimumreceiver of the general expression when L tends towards N. It istherefore important to choose a value for L which is sufficiently highin order to have an acceptable error rate.

The invention also consists of using a recursive algorithm fordetermining the suboptimum sequence α₀, . . . , α_(N-1).

More specifically the invention relates to a process for the noncoherentdemodulation of a signal y(t) where each symbol α_(k) has the sameenergy, said signal y(t) consisting of a signal x(t) on which issuperimposed a Gaussian white noise b(t), said signal x(t) beinglinearly modulated by a sequence of information symbols α₀, . . . ,α_(N-1) taken from an alphabet α, in which N is a non-zero integer, saidsymbols being emitted at successive dates separated by a time intervalT, said signal x(t) being centered on a carrier frequency f₀, whereinthe process comprises processing the signal y(t) to obtain N datablocks, z_(k),k-1, . . . , z_(k),k-L, in which L is a non-zero integerand 0≦k≦N-1, said data being defined for 1≦l≦L, by z_(k),k-l=r_(k).r_(k-l) * on which r*_(k-l) is the conjugate complex of r_(k-l)and in which r₀, . . . , r_(N-1) is a sequence of observationscontaining all the information of the signal y(t), maximizing a quantityV(α₀, . . . , α_(N-1)) in which α₀ . . . , α_(N-1) is a sequence ofsymbols of the alphabet α, said quantity being equal to ##EQU10## inwhich Re signifies "real part of" and α*_(k-l) is the conjugate complexof α_(k-l), and in which the index k-l is between 0 and N-1, saidmaximization being obtained by a recursive algorithm.

According to a secondary feature of the process according to theinvention, the processing of signal y(t) comprises the followingsuccessive actions:

the complex envelope r(t) of signal y(t) is extracted,

there is a matched filtering of the signal r(t),

the filtered signal is sampled at N successive dates separated by a timeinterval T so that the observations r₀, r₂, . . . r_(N-1) are obtained,

the L data on each of the N data blocks z_(k),k-1, . . . , z_(k).k-L arecalculated as a function of the observations r₀, r₂, . . . , r_(N-1).

According to another secondary feature of the process according to theinvention, in which the modulated signal is of the minimum shift keyingor phase shift keying type, the processing of the signal y(t) comprisesthe following successive actions:

a signal z(t) is produced by carrying out a pass band filtering of thesignal y(t) about the carrier frequency f₀,

the delayed signals z(t-T), z(t-2T), . . . , z(t-LT), are produced,

the signals z(t).z(t-T), z(t).z(t-2T), . . . , z(t).z(t-LT) areproduced,

these signals are sampled at the same time at successive dates separatedby a time interval T, so that at the kth sampling, a block of L dataz_(k),k-1, . . . , z_(k),k-L is obtained.

According to another secondary feature of the process according to theinvention, the recursive algorithm is the Viterbi algorithm.

According to another secondary feature of the process according to theinvention, only a subset of states in the sense of the Viterbi algorithmis retained at each sampling date.

According to another feature of the process according to the invention,only the state whose total metric in the sense of the Viterbi algorithmis the highest is retained at each sampling date.

The invention also relates to a demodulator for performing the processaccording to the invention and comprising in series:

a processing means receiving the signal y(t) and successively supplyingN blocks of L data z_(k),k-1, z_(k),k-2, . . . , z_(k),k-L in which0≦k≦N-1,

a calculating means supplying in view of the data of said N data blocksand in accordance with a recursive algorithm, a sequence of symbols α₀,. . . , α_(N-1) maximizing the quantity V(α₀, . . . , α_(N-1)).

According to a preferred embodiment of the demodulator according to theinvention, the processing means comprises in series:

an oscillator means receiving at the input the signal y(t) and supplyingat the output at least one signal describing the complex envelope r(t)of the signal y(t),

a matched filter,

a sampling means supplying observations r₀, r₁, . . . , r_(N-1), at Nsuccessive dates separated by time interval T,

A multiplier means receiving said observations and supplying N blocks ofL data z_(k),k-1, z_(k),k-2, . . . , z_(k),k-L in which 0≦k≦N-1.

According to an advantageous embodiment of the demodulator according tothe invention, for demodulating a signal y(t) of the minimum shiftkeying or phase shift keying type, the processing means comprises:

a reception band pass filter centred on the frequency f₀ and supplying asignal z(t),

L delay means in series, each supplying with a delay T the signalapplied to their input, the first delay means receiving the signal z(t),

L multipliers each for multiplying the signal z(t) by the signalsupplied by one of the said L delay means,

L low pass filters of cut-off frequency f₀, each being connected to theoutput of one of the said L multipliers,

a sampling means receiving in parallel on L inputs, the signals fromsaid L low pass filters and supplying, at N successive dates separatedby a time interval T, a block of L data z_(k),k-1, z_(k),k-2, . . . ,z_(k),k-L in which 0≦k≦N-1.

According to a preferred embodiment of the demodulator according to theinvention, the calculating means is able to perform a Viterbi algorithm.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is described in greater detail hereinafter relative tonon-limitative embodiments and the attached drawings, wherein show:

FIG. 1 already described, diagrammatically a modulation, demodulationand transmission chain of known construction.

FIG. 2 a lattice used in the Viterbi algorithm used in the processaccording to the invention.

FIG. 3 a simplified flow chart of the Viterbi algorithm used in theprocess according to the invention.

FIG. 4 a first embodiment of a demodulator according to the invention.

FIG. 5 a second embodiment of a demodulator according to the invention.

FIG. 6 a graph illustrating the performance characteristics of theprocess according to the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The demodulation process according to the invention is applicable to alllinearly modulated signals and with energy by constant symbol, i.e. toall signals whose complex envelope is in the form ##EQU11## as statedhereinbefore.

In exemplified manner, a description will be given of the demodulationprocess of a displaced modulation signal. This modulation is a specialtype of linear modulation. The complex envelope α(t) is of a displacedmodulation signal

has the general expression ##EQU12## in which ##EQU13## (energy perconstant symbol) and N₁ is the integral part of 1/2(N-1).

A minimum shift keying modulation is also defined by

    g(t)=cos (πt/2T)

for tε[-T,T]

    α.sub.m =(-1).sup.m-1.α.sub.m-1.a.sub.m-1

for m so that 1≦m≦N-1 and α₀ =1 for example and by αε[-1,1].

This modulation can also be expressed in the form of a continuous phasefrequency modulation, in which α(t) is expressed by ##EQU14## in whichtε[nT, (n+1)T] and θ is defined by the recurrence relation θ_(n)=θ_(n-1) +a_(n-1).(π/2).

With the following observations, ##EQU15## the quantity V(α₀, . . . ,α_(N-1)) is written ##STR2## This quantity can be maximized by arecursive algorithm so that on writing it is possible to write L_(K)=L_(K-1) +m(α_(K),S_(K-1),r_(K) . . . , r_(K-l)) by setting ##EQU16## inwhich S_(K-1) is called state at date K-1 and corresponds to the L-uplet(α_(K-1), . . . , α_(K-L)) and in which m(α_(K),S_(K-1),r_(K), . . . ,r_(K-L)) is called branch metric between states S_(K-1) and S_(K).

The expression of L_(K) as a function of L_(K-1) shows that theknowledge of the state S_(K) is possible as from S_(K-1). It istherefore possible to maximize V(α₀, . . . , α_(N-1)) by a recursivealgorithm. The process according to the invention advantageously usesthe Viterbi algorithm, which will now be briefly described. Thisalgorithm is described more completely in the Article "The Viterbialgorithm" by G. David Forney, Jr, which appeared in the proceedings ofthe IEEE, vol. 61, no. 3, March 1973, pp. 268-278.

FIG. 2 shows a lattice illustrating the performance of the Viterbialgorithm. In general terms, said lattice has n(α)^(L) states, in whichn(α) is the number of elements of the alphabet α. In the particular casedescribed, α={-1,1} and therefore n(α)=2. Moreover, as an example L=2 istaken. Thus, this lattice has four possible states S₁, S₂, S₃, and S₄ ateach date K-1, K, K+1, . . .

In FIG. 2, the dotted line transitions correspond to the symbol -1 ofthe alphabet α and those in continuous line form correspond to thesymbol +1 of the alphabet α. More specifically, the line designated 26corresponds to α_(K-1) =1 and the state designated 28 is S_(K). It isequal to (α_(K-2),α_(K-1)) i.e. to S₁ =(-1,-1). A branch metric mcorresponds to each transition between a state at a given date and thestate at the following date. The more probable the probablecorresponding transition the higher said metric. The Viterbi algorithmconsists of choosing within the lattice a path, i.e. a succession ofstates, so that the total metric equal to the sum of the branch metricslinking two successive states of said path is at a maximum. A singlepath arriving at each state is retained. The path associated with eachstate is also called the survivor, and can be simply represented by allthe successive symbols constituting it.

A description will now be given of a simplified flow chart of theViterbi algorithm. The first stage 30 is a stage of initializingmetrics, survivors and the recursiveness index K. The following stage 32consists of sampling the filtered signal r(t), which takes place at dateK.T.

Stages 34 and 36 perform the calculation of the branch metrics betweendates K-1 and K. Stage 34 consists of calculating the terms z_(K).K-1, .. . , z_(K),K-L respectively equal to Re(r_(K).r*_(K-1)), . . . ,Re(r_(K).r*_(K-L)) which appear in the expression of the branch metrics.When these calculations have been carried out, stage 36 calculates thebranch metrics linking each of the states at date K-1 with each of thestates at date K.

Stage 38 then peforms a choice between the n(α) total metrics reachingeach state at date K. For each state, the largest of these metrics isretained. The path whose metric is largest, called the survivor, is alsoretained.

In stage 40, the symbol α_(K-D) is decided, i.e. a value of the alphabetα is attributed to the symbol α_(K-D), in which D is an integer calledthe decision delay. This decision is made as a function of the resultsof stage 38. More specifically, at date K is chosen the survivor amongthe n(α)^(L) survivors having the largest metric. This survivor is asequence of symbols . . . , α_(K-D), . . . , α_(K-L), . . . , α_(K-1),α_(K). The value of the corresponding symbol in the chosen survivor isattributed to symbol α_(K-D).

In stage 42, it is tested whether the algorithm is ended. This is thecase if K is equal to N. If K is lower than N, K is increased and stages32, 34, 36, 38 and 40 are repeated.

Stages 34 and 36 can call for large-scale calculations, if the numbern(α) of elements of the alphabet α or the number L is high. It ispossible to reduce the practical complexity of the algorithm by onlyretaining at each date K one subset of the states of the lattice,instead of retaining all of them.

The states retained, can e.g. be those whose distance, in the Hammingsense, in the state corresponding to the largest total metric is below apredetermined value d. This known distance is equal to the sum of thedifferent symbols between two states. For example, the Hamming distancebetween states S₁ and S₂ of FIG. 2 is equal to 1 and the distancebetween states S₂ and S₃ is equal to 2.

In another embodiment of the algorithm, only one survivor may beretained at each state K. This known procedure is called "decision inthe loop".

The demodulation process according to the invention is performed in ademodulator, whose first embodiment is shown in FIG. 4. This demodulatorcomprises a processing means 13, a calculating means 54 and a decodingmeans 24. The processing means 13 comprises an oscillator 14 and a phaseshifter 16, which thus supplies two signals 2.cos (w₀ t+θ(t) and -2.sin(w₀ t+θ(t)). These signals are modulated by the signal y(t) and at theoutput the signals Re(r(t)) and Im(r(t)) are obtained, in which thesignal r(t) is the complex envelope of the signal y(t). The signals areapplied to the input of a filter 18 of pulse response g(t₀ -t), in whicht₀ characterizes the duration of the transmission and g(t) is the pulseresponse of the emission filters of the demodulator supplying theemitted signal x(t). A sampling means 20, in series with filter 18,switched at N dates separated by a time interval T supplies the datapairs Re(r_(k)) and Im(r_(k)) in which 0≦k≦N-1. A multiplier meansreceives the data pairs and supplies blocks of L data z_(k),k-1, . . . ,z_(k),k-L in which 0≦k≦N-1, which are received by the calculating means54, which is able to realize the Viterbi algorithm. Calculating means 54can in particular be a signal processing processor containing amicroprogram able to realize the Viterbi algorithm. Examples ofprocessors which can be used for calculating means 54 are uPTS ofC.N.E.T., TMS 320 of Texas Instruments or NEC 7720 of NationalSemiconductor.

Finally, the demodulator can comprise a decoding means 24 receiving thesequence of symbols α₀, . . . , α_(N-1) supplied by calculating means 54and delivering the sequence of symbols α₀, . . . , α_(N-1) elements ofthe alphabet A if, on modulation, the reverse coding was used.

The demodulator according to the invention described with reference toFIG. 4 has a general structure making it possible to process alllinearly modulated signals. In certain types of linear modulations, itis possible to have a simpler modulator. With reference to FIG. 5, ademodulator for signals will now be described of the minimum shiftkeying modulation type.

The demodulator comprises a processing means 13 receiving the signaly(t) and supplying blocks of L data z_(k),k-1, . . . , z_(k),k-L inwhich 0≦k≦N-1, a calculating means 54 and a decoding means 24. These twolatter means are identical to those used in the demodulator describedwith reference to FIG. 4, so that they will not be described again.

Processing means 13 comprises a band pass filter 44 centred about thefrequency f₀, which supplies a signal z(t). It then comprises L delaymeans 46₁, . . . , 46_(L) in series, the first delay means 46₁ receivingz(t). Each of these delay means delays the signal applied to its inputby a time T. In the described case of a displaced modulation signal ofthe minimum shift keying type, said delay T is linked with the ripplew₀, in which W₀ =2πf₀ by w₀.T=π/2p in which p is an integer. The signalsupplied by each delay means is modulated by the signal z(t) inmultipliers 48₁, . . . , 48_(L). At the output of each of the latter, isconnected a low pass filter 50₁, . . . , 50_(L) of cut-off frequency f₀.A sampling means 52 with L inputs receives in parallel the signals fromsaid low pass filters. At N successive dates separated by a timeinterval T, it supplies a block of L data z_(k),k-1, z_(k),k-2, . . .z_(k),k-L, in which 0≦k≦N-1. The data are then supplied to the L inputsof the calculating means 54.

It should be noted that the demodulator can be used for phase shiftkeying modulation signals. It is merely necessary to replace the delay Tof each delay means by a delay T' proving w₀.T'=2pπ in which p is aninteger.

FIG. 6 is a graph illustrating the performance characteristics of thedemodulation process according to the invention. On the abscissa appearsthe energy ratio per bit (E_(b)) at the monolateral spectral density N₀on the transmission channel, said quantity being measured in watt/hertz.On the ordinate, on a semilogarithmic axis, appears the error rate atreception.

The curves are demodulation performance curves of a linearly modulatedsignal with minimum shift keying. The noncoherent demodulation has beenrealized by a receiver using the Viterbi algorithm.

Curve C_(TH) corresponds to a theoretical coherent receiver andconstitutes the optimum curve. The following curve C corresponds to acoherent receiver simulated by the same transmission chain and curvesNC₁, . . . , NC₅ corresponds to various noncoherent receivers accordingto the invention. The index of each curve NC represents the value ofvariable L. It can be seen that with a value L equal to 5, a noncoherentreceiver is obtained, whose performance characteristics are close tothose of a conventional coherent receiver.

What is claimed is:
 1. A process for the noncoherent demodulation of asignal y(t), said signal y(t) consisting of a signal x(t) on which issuperimposed a Gaussian white noise b(t), said signal x(t) beinglinearly modulated by a sequence of information symbols α₀, . . . ,α_(N-1) taken from an alphabet α, in which N is a nonzero integer, saidsymbols being emitted at successive dates separated by a time intervalT, said signal x(t) being centered on a carrier frequency f₀, whereinthe process comprises processing the signal y(t) to obtain N datablocks, z_(k),k-1, . . . , z_(k),k-L, in which L is a non-zero integerand 0≦k≦N-1, said data being defined for 1≦l≦L, by z_(k),k-l=r_(k).r_(k-l) * on which r*_(k-l) is the conjugate complex of r_(k-l)and in which r₀, . . . , r_(N-1) is a sequence of observationscontaining all the information of the signal y(t), maximizing a quantityV(α₀ , . . . , α_(N-1)) in which α₀, . . . , α_(N-1) is a sequence ofsymbols of the alphabet α, said quantity being equal to ##EQU17## inwhich Re signifies "real part of" and α*_(k-l) is the conjugate complexof α_(k-l), and in which the index k-l is between 0 and N-1, saidmaximization being obtained by a recursive algorithm.
 2. A processaccording to claim 1, wherein the processing of the signal y(t)comprises the following successive actions:the complex envelope r(t) ofthe signal y(t) is extracted, there is a matched filtering of the signalr(t), the filtered signal is sampled at N successive dates separated bya time interval T so that the observations r₀, r₂, . . . , r_(N-1) areobtained, the L data on each of the N data blocks z_(k),k-1, . . . ,z_(k),k-L are calculated as a function of the observations r₀, r₂, . . ., r_(N-1).
 3. A process according to claim 1, in which the modulatedsignal is of the minimum shift keying or phase shift keying type,wherein the processing of the signal y(t) comprises the followingsuccessive actions;a signal z(t) is produced by carrying out a pass bandfiltering of the signal y(t) about the carrier frequency f₀, the delayedsignals z(t-T), z(t-2T), . . . , z(t-Lt) are produced, the signalsz(t).z(t-T), z(t).z(t-2T), . . . , z(t).z(t-LT) are produced, thesesignals are sampled at the same time at successive dates separated by atime interval T, so that at the kth sampling a block of L dataz_(k),k-1, . . . , z_(k),k-L is obtained.
 4. A process according toclaim 1, wherein the recursive algorithm is the Viterbi algorithm.
 5. Aprocess according to claim 4, wherein only one subset of states in thesense of the Viterbi algorithm is retained at each sampling date.
 6. Aprocess according to claim 5, wherein only the state whose total metric,in the sense of the Viterbi algorithm is largest is retained at eachsampling date.
 7. A demodulator for the noncoherent demodulation of areceived signal y(t) to retrieve a sequence of emitted informationsymbols α₀, α₁ , . . . , α_(N-1) taken from an alphabet α in which N isa non-zero integer, said symbols being made to modulate a carrier signalat successive dates separated by a time interval T to create an emittedsignal x(t), said received signal y(t) being a combination of saidemitted signal x(t) and of a white Gaussian noise signal b(t), whereinsaid demodulator comprises in series:a processing means receiving saidsignal y(t) and successively supplying N blocks of L data z_(k),k-1,z_(k),k-2, . . . , z_(k),k-L in which 0≦k≦ N-1, in which each data is aproduct of samples of demodulated signal y(t), a calculating meanssupplying in view of the data of said N data blocks and in accordancewith a recursive algorithm, a sequence of symbols α₀, . . . , α_(N-) 1maximizing ##EQU18## said sequence of symbols α₀, α₁, . . . , α_(N-1)being identified as the sequence of emitted symbols α₀, α₁, . . . ,α_(N-1).
 8. A demodulator according to claim 7, wherein the processingmeans comprises in series:an oscillator means receiving at the inputsaid signal y(t) and supplying at the output at least one signalcorresponding to a complex envelope r(t) of said signal y(t), a matchedfilter, a sampling means supplying, sampling values of signal r(t), orobservations, r₀, r₁, . . . , r_(N-1), at N successive dates separatedby time interval T, a multiplier means receiving said observations andsupplying N blocks of L sequences of data z_(k),k-1, z_(k),k-2, . . . ,z_(k),k-L, in which 0≦k≦N-1, and z_(k),k-l =r_(k). r*_(k-l) (1≦l≦L),r*_(k-l) being the complex conjugate of r_(k-l).
 9. A demodulatoraccording to claim 7 for demodulating a signal y(t) of the Minimum ShiftKeying or Phase Shift Keying type, wherein the processing meanscomprises:a reception band pass filter centered on the frequency of thecarrier signal used on emission side, and supplying a signal z(t), Ldelay means in series, each supplying with a delay T the signal appliedto their input, the first delay means receiving the signal z(t), Lmultipliers each for multiplying the signal z(t) by the signal suppliedby a respective one of said L delay means, L low pass filters withcut-off frequency equal to the frequency of the carrier signal used onthe emission side, each low pass filter being connected to the output ofone of the said L multipliers, a sampling means receiving in parallel onL inputs the signals from said L low pass filters and supplying a Nsuccessive dates separated by a time interval T, a block of L dataz_(k),k-1, z_(k),k-2, . . . , z_(k),k-L in which 0≦k≦N-1.
 10. Ademodulator according to claim 7, wherein the calculating means is ableto realize a Viterbi algorithm.